[ncl-talk] Need a solution for calculate Determinant of a (rather) large matrix

[Lam Hoang]

Dear Dennis,
uname -a gives:

Darwin MACBooks-MBP 16.7.0 Darwin Kernel Version 16.7.0: Thu Jan 11
22:59:40 PST 2018; root:xnu-3789.73.8~1/RELEASE_X86_64 x86_64

and gcc --version gives:


Configured with: --prefix=/Applications/Xcode.app/Contents/Developer/usr
--with-gxx-include-dir=/usr/include/c++/4.2.1

Apple LLVM version 8.1.0 (clang-802.0.42)

Target: x86_64-apple-darwin16.7.0

Thread model: posix

InstalledDir:
/Applications/Xcode.app/Contents/Developer/Toolchains/XcodeDefault.xctoolchain/usr/bin


anything looks suspicious?
Regards,


On Tue, Jul 10, 2018 at 8:59 PM, Dennis Shea <shea at ucar.edu> wrote:

> Normally, NCL would use an LAPACK code to compute a mathematical quantity.
> However, LAPACK contains no such subroutine due to issues with accuracy and
> stability:
>
>        http://www.netlib.org/lapack/faq.html#_are_there_routines_
> in_lapack_to_compute_determinants
>
> Really, 'they' (applied mathematicians) do not want people calculating the
> determinant.
> ===
>
> NCL uses a computer program from:
>
>     An Introduction to  Computational Physics, Tao Pang (Cambridge
> University Press,1997).
> ===
>
> The use of integer or float values as input should have no effect. All
> non-double input is promoted to double prior to input to the fortran code
> used to perform the calculations.
>
> I have no idea why you are encountering extremely long execution times. My
> 6.3.0 [MAC] returns a result more or less immediately. What version of gcc
> do you have installed? Please send the output from the following:
>
> %> uname -a
>
> %> gcc --version
>
> ====
> That said:  I have tried to calculate the determinant with N=41
>
>    N = 41
>    x = random_uniform(0,5,(/N,N/))
>    d = determinant(x)                          ; VERY fast; instantaneous
> return value
>    print(d)
>
> Variable: d
> Type: float
> Total Size: 4 bytes
>             1 values
> Number of Dimensions: 1
> Dimensions and sizes:   [1]
> Coordinates:
> (0)
>
> *1.767279e+31       <====  ????  I have no idea what the correct answer is*
> Ummm, rather large number!!!
>
> ====
> I will open a JIRA trouble ticket and ask the core NCL developers if
> everything looks good.
>
> ====
> Again, echoing LAPACK, calculating a determinant has issues.
>
> Regards
>
> On Tue, Jul 10, 2018 at 6:34 AM, Lam Hoang <lamhpvn at gmail.com> wrote:
>
>> Dear all,
>> I want to calculate determinant of a 41x41 real (float) matrix. I used
>> determinant() function
>> https://www.ncl.ucar.edu/Document/Functions/Built-in/determinant.shtml
>>
>> However it is very slow.
>>
>> I try to run the sample in the above page, it's quick. Even if I replace
>> integer values by float values (i.e replace 1 by 1.0, 0 by 0.0 and so on)
>> I try to create a 4x4 real matrix, give all members a value of 1.0
>> It seems that the determinant() function runs forever and does not return
>> any value
>>
>> In the following illustration, a is sample matrix after replacing integer
>> by float values. It takes NCL few seconds to return the value d = 30
>>
>> x is new 4x4 matrix created by my new() function, it never gives me any
>> result.
>>
>> *Variable: a*
>>
>> *Type: float*
>>
>> *Total Size: 64 bytes*
>>
>> *            16 values*
>>
>> *Number of Dimensions: 2*
>>
>> *Dimensions and sizes: [4] x [4]*
>>
>> *Coordinates: *
>>
>> *(0) d = 30*
>>
>>
>> *Variable: x*
>>
>> *Type: float*
>>
>> *Total Size: 64 bytes*
>>
>> *            16 values*
>>
>> *Number of Dimensions: 2*
>>
>> *Dimensions and sizes: [4] x [4]*
>>
>> *Coordinates: *
>>
>>
>>
>> Any suggestion or solution for this?
>>
>> Regards,
>>
>>
>> p/s: I am using NCL v6.3.0
>>
>> --
>> Lam Hoang, PhD
>> Chief of Climate Prediction Division,
>> Viet Nam National Center of Hydro-Meteorology Forecasting
>> National Hydro-Meteorological Services of Vietnam
>> 8 Phao Dai Lang street, Lang Thuong, Dong Da, Ha Noi, Vietnam
>> <https://maps.google.com/?q=8+Phao+Dai+Lang+street,+Lang+Thuong,+Dong+Da,+Ha+Noi,+Vietnam&entry=gmail&source=g>
>> Mob: +84 9 682 34 682
>>
>> Associate Researcher,
>> School of Earth, Atmosphere and Environment
>> Monash University, VIC 3800
>> Email: lam.hoang at monash.edu
>>
>> _______________________________________________
>> ncl-talk mailing list
>> ncl-talk at ucar.edu
>> List instructions, subscriber options, unsubscribe:
>> http://mailman.ucar.edu/mailman/listinfo/ncl-talk
>>
>>
>


-- 
Lam Hoang, PhD
Chief of Climate Prediction Division,
Viet Nam National Center of Hydro-Meteorology Forecasting
National Hydro-Meteorological Services of Vietnam
8 Phao Dai Lang street, Lang Thuong, Dong Da, Ha Noi, Vietnam
Mob: +84 9 682 34 682

Associate Researcher,
School of Earth, Atmosphere and Environment
Monash University, VIC 3800
Email: lam.hoang at monash.edu
-------------- next part --------------
An HTML attachment was scrubbed...
URL: <http://mailman.ucar.edu/pipermail/ncl-talk/attachments/20180710/d8f4a3d2/attachment.html>